TALO Interpolation & Extrapolation App (Android & IOS)

Interpolation & Extrapolation App

by TALO-tech

 

Introduction

Interpolation & Extrapolation is another small App & useful tool developed by TALO-tech, interpolation & extrapolation calculations which is known also as [Pro-rata (proportionate allocation)], which is common between Engineers, Accounts & Estimators fields...

   Extrapolation is an estimation of a value based on extending a known sequence of values beyond the area that is certainly known... "In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points" from Wikipedia, Interpolation is an estimation of a value within two known values in a sequence of values

How to use the Interpolation & Extrapolation App

The entry page is consists of 2 Columns & 3 rows, each row presents the point value, the Columns are divided to X columns (All Known Values) & Y Columns (2 values are known only)... the user can choose between Y1,Y2, or Y3 as the unknown value the App will do the calculation without the need to press a button.... the result value will be shown in a RED color

Linear interpolation (from wikipedia)

One of the simplest methods is linear interpolation (sometimes known as lerp). Consider the above example of estimating f(2.5). Since 2.5 is midway between 2 and 3, it is reasonable to take f(2.5) midway between f(2) = 0.9093 and f(3) = 0.1411, which yields 0.5252.

Generally, linear interpolation takes two data points, say (x_a,y_a) and (x_b,y_b), and the interpolant is given by

${\displaystyle y=y_{a}+\left(y_{b}-y_{a}\right){\frac {x-x_{a}}{x_{b}-x_{a}}}{\text{ at the point }}\left(x,y\right)}$

${\displaystyle {\frac {y-y_{a}}{y_{b}-y_{a}}}={\frac {x-x_{a}}{x_{b}-x_{a}}}}$

${\displaystyle {\frac {y-y_{a}}{x-x_{a}}}={\frac {y_{b}-y_{a}}{x_{b}-x_{a}}}}$

This previous equation states that the slope of the new line between ${\displaystyle (x_{a},y_{a})}$ and ${\displaystyle (x,y)}$ is the same as the slope of the line between ${\displaystyle (x_{a},y_{a})}$ and ${\displaystyle (x_{b},y_{b})}$

Linear interpolation is quick and easy, but it is not very precise. Another disadvantage is that the interpolant is not differentiable at the point x_k.

The following error estimate shows that linear interpolation is not very precise. Denote the function which we want to interpolate by g, and suppose that x lies between x_a and x_b and that g is twice continuously differentiable. Then the linear interpolation error is

${\displaystyle |f(x)-g(x)|\leq C(x_{b}-x_{a})^{2}\quad {\text{where}}\quad C={\frac {1}{8}}\max _{r\in [x_{a},x_{b}]}|g''(r)|.}$

In words, the error is proportional to the square of the distance between the data points. The error in some other methods, including polynomial interpolation and spline interpolation (described below), is proportional to higher powers of the distance between the data points. These methods also produce smoother interpolants.

 

Introduction Video

 Link of Interpolation & Extrapolation App

Apple Store link will be updated soon

Contact Us

for any problems, suggestions, please contact us on 

talotech.engtools@gmail.com

TALO-tech Team